Question to Finance Gurus (& investors)

[JayB]

As the topic title mentions, this one is to Finance gurus, I expect users who would answer my question to have some advanced understanding about the different methods used to price an asset (i.e. stocks).

So as you know guys in valuing the intrinsic value of an asset to a diversified individual investor, one element used in the CAPM model, is the stock's beta and the market's risk premium, which together capture the risk of a certain asset. And risk in finance is described as the standard deviation between actual vs. expected return, or in other words, how much a certain stock's return deviates from its expected return (the more it deviates the more risky an asset is perceived to be).

But isn't this illogical? why would stock A, which deviates more than stock B (both having the same expected return) be priced in such a way as to generate higher returns?

To put you in the same state of mind as me, think of the following:

Suppose that I am about to sell two different tickets, one that entitles its bearer to earn 1$ every time I toss a coin for 10 consecutive tosses no matter the outcome (whether heads or tails), and the other 2$ every time the outcome is heads but nothing for tails. And so I put these two tickets in the open market so that investors can bid on them.

In finance, the latter is a more risky investment and thus current finance theory suggests that the market would price it at a lower price point than the former, being “Risk free”. But if this was the case, then everyone would rush to buy the latter ticket, after all, why would the ticket with a certain payoff be priced more expensively than that of an uncertain one if they both have the same expected return? (especially to a diversified investor)

Notice that both have an expected return of 10$, and so my theory says that eventually, they will be both priced in the market at the same price point (a little less than 10$ per ticket).

This is all to suggest that risk in finance should be measured in a different way, what do you guys think?

[PYneer]

I'm having a really hard time trying to figure out what you are trying to say since I think you've basically answered your question. But if I understood your question correctly, it basically boils down to this?

why would stock A, which deviates more than stock B (both having the same expected return) be priced in such a way as to generate higher returns?

The one with more volatility is more expensive because buyer has to compensate the bearer's risk by paying a risk premium (which you mentioned). More explanation later.

In finance, the latter is a more risky investment and thus current finance theory suggests that the market would price it at a lower price point than the former, being “Risk free”.
....
why would the ticket with a certain payoff be priced more expensively than that of an uncertain one if they both have the same expected return?

Well because it doesn't and it's not true. CAPM is a measure of return not a measure of risk and the formula does not take volatility into factor.

Even though their expected return are the same, their actual return will/should be different. ie 1$ coin toss gets you 10$ in the end but 2$ could give you 20$ or nothing. Since there is a chance to to earn more than the risk free alternative, some people are willing to basically gamble for a higher return and buyers often have to pay a premium for the risk the owner has taken.

To illustrate, look at bond yields & bond rates. As the maturity increases, yields changes more volatile because of more uncertainty even though the systematic risk is the same.

This is all to suggest that risk in finance should be measured in a different way, what do you guys think?

CAPM is one of the more simpler models for simple estimates. Different asset classes have different and more complex models already exists and are used.

[JayB]

The one with more volatility is more expensive because buyer has to compensate the bearer's risk by paying a risk premium (which you mentioned). More explanation later.

Dude that's exactly what I'm arguing against.

I'm arguing that volatility shouldn't be a factor of risk, nor should it be a reason for asking for more return. I gave the coin tossing as an example, stating that both tickets that entitle you for the earnings of the tosses should be priced the same. And I showed how differences in their prices will make the cheaper more attractive.

Well because it doesn't and it's not true. CAPM is a measure of return not a measure of risk and the formula does not take volatility into factor.

Off-course it does. It is captured by the "beta" in the formula, which basically calculates how volatile an asset is relative to the market. And the market volatility itself has a return that is captured in the market risk premium.

Even though their expected return are the same, their actual return will/should be different. ie 1$ coin toss gets you 10$ in the end but 2$ could give you 20$ or nothing. Since there is a chance to to earn more than the risk free alternative, some people are willing to basically gamble for a higher return and buyers often have to pay a premium for the risk the owner has taken.

Well that's my whole point, I'm arguing that two assets having the same expected return should be priced the same no matter how much their actual return deviates from their expected return.

Look the return rates are set by diversifies investors (mutual funds, hedge funds etc...), off-course if they buy 1 coin paying 2$ or nothing, they might have some risk (although I bet they'd prefer that to buying the risk-free coin), but when you buy 1000 coins, you eliminate the risk (this is what they actually do by buying a big number of stocks).

My arguments lead to the following conclusion: Even if the risk premium was 1% or 2% (as opposed to 5 - 6% nowadays) rational investors would still be better off buying volatile assets and run away from risk-free assets promising a lower return. And with time this is what I think will actually happen. Risk premium will go down and investors will still invest in risky assets.

CAPM is one of the more simpler models for simple estimates. Different asset classes have different and more complex models already exists and are used.

I know but that's irrelevant to my discussion as risk in finance is always calculated in the same way (volatility).

My argument is that volatility is not how risk should be calculated.

[PYneer]

I'm arguing that two assets having the same expected return should be priced the same no matter how much their actual return deviates from their expected return.

Both expected returns are the same so maybe more people will choose the risk free option in that case. But their actual return will be different in the scenarios you've provided and variation alone can cause the pricing to be different (explained next).

It is captured by the "beta" in the formula

The beta only standardized the risk but doesn't necessarily factors in the volatility. It only provides insight to systematic risk but does not factor in non-diversiable risk that is specific to 2$ coin toss that 1$ does not have.

rational investors would still be better off buying volatile assets and run away from risk-free assets promising a lower return.

Maybe in the long run, holding risky assets MIGHT provide a higher return if the market is good. But on the other hand the more volatile asset will lose more if market is bad. eg. Comparison between stocks and bonds. Stocks should have a higher expected return and more volatile as bonds are usually treated as risk free assets. When times are good and everything goes up, stocks out performs bonds. But as soon as market is bad, bond outperforms stocks.

I know but that's irrelevant to my discussion as risk in finance is always calculated in the same way (volatility).

It's pretty relevant since other models incorporate volatility and risks whereas CAPM doesn't. For example, the popular Black-Scholes model has sigma in addition to risk rate in order to factor in volatility.

My argument is that volatility is not how risk should be calculated.

Fine, tell us how it should be calculated then. Honestly, I don't even know what to say anymore since this is literally basic finance stuff.